![12 31 Given a matrix A = (a) (40 pts) Compute the inverse of matrix A by: + Solving Ax=b with b set to [1, 0]T and [0, 1]T +](http://img.homeworklib.com/questions/86d1c340-6422-11eb-a14c-33a6a3c4e6cd.png?x-oss-process=image/resize,w_560)
Homework Answers
ANSWER:--
GIVEN
THAT:--![all briven A=[ů [io]? [å } ] Consider the system AX= b where b = n [ü }] [] -0.] - 244 +372 = 1 (12 44+5 ₂ = 0 -. (2) (2) -](http://img.homeworklib.com/questions/c48b06d0-bf1c-11eb-9ca4-0922d50a0acd.png?x-oss-process=image/resize,w_560)
![fum ( 2 ) () •2 ][!]-H) .. a--512 10=2 :9 3/ d=-). 1 ..^^ = [et] [-] carton) - using (reusian elimination with partial piroto](http://img.homeworklib.com/questions/c53025d0-bf1c-11eb-8893-91ccd820c63a.png?x-oss-process=image/resize,w_560)
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12 31 Given a matrix A = (a) (40 pts) Compute the inverse of matrix A...
7. Let A [aij] be an n x n invertible tridiagonal matrix, that is aij= 0 if |i - j > 1. Compute the number of operat...
7. Let A [aij] be an n x n invertible tridiagonal matrix, that is aij= 0 if |i - j > 1. Compute the number of operations needed to solve the system Ax b by Gauss elimination without partial pivoting. (10 marks)
7. Let A [aij] be an n x n invertible tridiagonal matrix, that is aij= 0 if |i - j > 1. Compute the number of operations needed to solve the system Ax b by Gauss elimination without...
2. (a) Let A be the matrix A -4 21 8 -40 Write down the 3 x 3 permutation matrix P such that PA interchanges the 1st and 3rd rows of A. Find the inverse of P. Use Gaussian elimination with partial pi...
2. (a) Let A be the matrix A -4 21 8 -40 Write down the 3 x 3 permutation matrix P such that PA interchanges the 1st and 3rd rows of A. Find the inverse of P. Use Gaussian elimination with partial pivoting to find an upper triangular matrix U, permutation matrices Pi and P2 and lower triangular matrices Mi and M2 of the form 1 0 0 Mi-1A1 10 a2 0 1 M2 0 0 0 b1 with ail...
1. [A] is the coefficient matrix for [Aj[X]-(C. 12-10 16 A-16 9 24 12 8 At the end of forward elimination steps of Gaussian Elimination method with partial pivoting, the coefficient matrix looks...
1. [A] is the coefficient matrix for [Aj[X]-(C. 12-10 16 A-16 9 24 12 8 At the end of forward elimination steps of Gaussian Elimination method with partial pivoting, the coefficient matrix looks like 0 0 by a) bs is most nearly (circle correct response) [10 pts.] A. -2.0298 B. 1.4167 C. 12.000 D. 22.667 b) This is a consistent/inconsistent system. (circle correct response) (5 points) A square matrix [A] is upper triangular if (circle correct response) |5 points (A)...
1. (5 pts) Use partial pivoting to compute (by hand) the PA -LU factorization of the matrix A-12-1 3
1. (5 pts) Use partial pivoting to compute (by hand) the PA -LU factorization of the matrix A-12-1 3
1. (5 pts) Use partial pivoting to compute (by hand) the PA -LU factorization of the matrix A-12-1 3
Problem X. Take the method for finding the inverse of a given n x n matrix A -a by straightforwar...
Problem X. Take the method for finding the inverse of a given n x n matrix A -a by straightforward Gauss (or Jordan) elimination (Problem 7 is a particular case for n 3). First you write down the augmented matrix A and apply the Gauss process to this as discussed in class: A-la2,1 a2,2 a2,n : an,1 an,2 .. an.n 0 0 1 3. Derive the Jordan elimination algorithm without pivoting for the augmented matrix in terms of a triple...
3. Given the matrix [ -1 2 -1] A= 3 2 1 10 10 1 Following...
3. Given the matrix [ -1 2 -1] A= 3 2 1 10 10 1 Following steps (a)(b) to obtain the LU decomposition of the matrix A with partial piv- oting (a) Apply the Gaussian elimination method with partial pivoting to obtain an upper trian- gular matrix U. Record the corresponding permutation matrix for each pivoting step, and the numbers lik used to eliminate the zeros in column k. (b) Based on (a), express the matrices P, L and U...
(5 points) The following augmented matrix is in reduced row echelon form. Decode from the matrix...
(5 points) The following augmented matrix is in reduced row echelon form. Decode from the matrix the solution of the corresponding system of linear equations (using the variables X1, X2, and x3) or state that the system is inconsistent. (if a free variable is needed use the parameter t.) 1 0 3121 0 1 53 Lo 0 olo) con (10 points) Use row operations to compute the inverse of the matrix A = [ 53 -2] and use it to...
ALTSIS AND NUMERICAL ANALYSIS 2. (a) Let A be the matrix 2 -115 8-4 Write down the 3 x 3 permutat...
ALTSIS AND NUMERICAL ANALYSIS 2. (a) Let A be the matrix 2 -115 8-4 Write down the 3 x 3 permutation matrix P such that PA interchanges the 1st and 3rd rows of A. Find the inverse of P Use Gaussian elimination with partial pivoting to find an upper triangular matix U, permutation matrices Pi and P2 and lower triangular matrices M and M2 of the form 1 0 0 0 1 1 0 0 0 bi 1 with land...
Problem 3. Matrix condition The Lower Colorado River consists of a series of four reservoirs as...
Problem 3. Matrix condition The Lower Colorado River consists of a series of four reservoirs as shown in Fig. P11.12. Mass balances can be written for each reservoir, and the following set of MENG 602/438 Hao-Chun Chiang simultaneous linear algebraic equations results: Ac=b [ 13.422 0 0 0 -13.422 12.252 0 0 0 - 12.252 12.377 0 0 -12.377 11.797 (750.5 300 102 30 where the right-hand-side vector consists of the loadings of chloride to each of the four lakes...
1) Consider the system of linear algebraic equations Ax = B where | 1 1/2 1/31...
1) Consider the system of linear algebraic equations Ax = B where | 1 1/2 1/31 1/2 1/3 1/4 11/3 1/4 1/5 a) Find x, A" and det(A) using Gauss-Jordan elimination without pivoting. b) Using the result of part (a), find the condition number of A based on the Euclidean (Frobenius) norm. How many digits of precision do you suspect are lost in the solution x due to ill-conditioning?
7. Let A [aij] be an n x n invertible tridiagonal matrix, that is aij= 0 if |i - j > 1. Compute the number of operations needed to solve the system Ax b by Gauss elimination without partial pivoting. (10 marks)
7. Let A [aij] be an n x n invertible tridiagonal matrix, that is aij= 0 if |i - j > 1. Compute the number of operations needed to solve the system Ax b by Gauss elimination without...
2. (a) Let A be the matrix A -4 21 8 -40 Write down the 3 x 3 permutation matrix P such that PA interchanges the 1st and 3rd rows of A. Find the inverse of P. Use Gaussian elimination with partial pivoting to find an upper triangular matrix U, permutation matrices Pi and P2 and lower triangular matrices Mi and M2 of the form 1 0 0 Mi-1A1 10 a2 0 1 M2 0 0 0 b1 with ail...
1. [A] is the coefficient matrix for [Aj[X]-(C. 12-10 16 A-16 9 24 12 8 At the end of forward elimination steps of Gaussian Elimination method with partial pivoting, the coefficient matrix looks like 0 0 by a) bs is most nearly (circle correct response) [10 pts.] A. -2.0298 B. 1.4167 C. 12.000 D. 22.667 b) This is a consistent/inconsistent system. (circle correct response) (5 points) A square matrix [A] is upper triangular if (circle correct response) |5 points (A)...
1. (5 pts) Use partial pivoting to compute (by hand) the PA -LU factorization of the matrix A-12-1 3
1. (5 pts) Use partial pivoting to compute (by hand) the PA -LU factorization of the matrix A-12-1 3
Problem X. Take the method for finding the inverse of a given n x n matrix A -a by straightforward Gauss (or Jordan) elimination (Problem 7 is a particular case for n 3). First you write down the augmented matrix A and apply the Gauss process to this as discussed in class: A-la2,1 a2,2 a2,n : an,1 an,2 .. an.n 0 0 1 3. Derive the Jordan elimination algorithm without pivoting for the augmented matrix in terms of a triple...
3. Given the matrix [ -1 2 -1] A= 3 2 1 10 10 1 Following steps (a)(b) to obtain the LU decomposition of the matrix A with partial piv- oting (a) Apply the Gaussian elimination method with partial pivoting to obtain an upper trian- gular matrix U. Record the corresponding permutation matrix for each pivoting step, and the numbers lik used to eliminate the zeros in column k. (b) Based on (a), express the matrices P, L and U...
(5 points) The following augmented matrix is in reduced row echelon form. Decode from the matrix the solution of the corresponding system of linear equations (using the variables X1, X2, and x3) or state that the system is inconsistent. (if a free variable is needed use the parameter t.) 1 0 3121 0 1 53 Lo 0 olo) con (10 points) Use row operations to compute the inverse of the matrix A = [ 53 -2] and use it to...
ALTSIS AND NUMERICAL ANALYSIS 2. (a) Let A be the matrix 2 -115 8-4 Write down the 3 x 3 permutation matrix P such that PA interchanges the 1st and 3rd rows of A. Find the inverse of P Use Gaussian elimination with partial pivoting to find an upper triangular matix U, permutation matrices Pi and P2 and lower triangular matrices M and M2 of the form 1 0 0 0 1 1 0 0 0 bi 1 with land...
Problem 3. Matrix condition The Lower Colorado River consists of a series of four reservoirs as shown in Fig. P11.12. Mass balances can be written for each reservoir, and the following set of MENG 602/438 Hao-Chun Chiang simultaneous linear algebraic equations results: Ac=b [ 13.422 0 0 0 -13.422 12.252 0 0 0 - 12.252 12.377 0 0 -12.377 11.797 (750.5 300 102 30 where the right-hand-side vector consists of the loadings of chloride to each of the four lakes...
1) Consider the system of linear algebraic equations Ax = B where | 1 1/2 1/31 1/2 1/3 1/4 11/3 1/4 1/5 a) Find x, A" and det(A) using Gauss-Jordan elimination without pivoting. b) Using the result of part (a), find the condition number of A based on the Euclidean (Frobenius) norm. How many digits of precision do you suspect are lost in the solution x due to ill-conditioning?
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